It has previously been proposed, see German Patent Disclosure Document DE-OS No. 36 01 539, to provide an apparatus to clean an offset cylinder of a printing machine. Offset cylinders sometimes collect dust, lint, and the like during operation. In accordance with this disclosure, brushes are periodically engaged with the offset cylinder. Thus, lint and the like is swept off the engaged cylinder and directed to a lint collector. The brush is arranged at the periphery of the respective cylinder and secured at both ends in the side walls of the printing machine. It has been found that this placement and arrangement is inconvenient and interferes with work on the machine.